The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for determining field maps for MRI.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the excited nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited nuclei or “spins”, after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
Accurate information about the magnetic fields employed during a given MRI process is, often, very important to securing clinically-useful images. For example, “magnetic field maps” or “field maps” are often created to record information about any deviations from the desired or ideal magnetic field that is caused by B0-field inhomogeneities, chemical shift inhomogeneities or susceptibility-induced inhomogeneities. Accurate field maps are of critical importance in numerous MR applications, including functional MRI (fMRI), MR thermometry, MR spectroscopy, and many quantitative MR methods.
Common approaches to computing the field maps typically rely on acquiring multiple scans with different echo times to discern information about the inhomogeneities that are present. Unfortunately, a fundamental accuracy-dynamic range trade-off exists with multi-echo field mapping; namely, a large difference between the echo times (TE) reduces the maximum detectable field offset value and causes phase wrapping (or aliasing), while a shorter TE yields unreliable measurements with high variance. To overcome the resulting inaccuracies, a class of spatio-temporal post-processing algorithms, termed “phase unwrapping,” has been proposed and developed. Specifically, the trade-off above could be summarized as follows: the actual phase signal could be any real number. However, the measured phase signal (or angle) can only be uniquely represented by values in a 2π range. A “wrapping” ambiguity occurs whenever the original phase signal exceeds 2π radians in any picture element (voxel). This happens in cases of (a) phase accumulation or (b) noise-induced phase accumulation. The unwrapping algorithms attempt to recover the original signal by determining the source of phase signal errors (wrapping, noise, or noise-induced phase wrapping). This ambiguity, however, can only be resolved under certain assumptions such as signal smoothness and no phase aliasing in regions known a priori.
Unfortunately, the imposition of a smoothness constraint on the measured data, reduces the spatial resolution of the measurements. Furthermore, the efficiency of these phase unwrapping algorithms often depends on the accuracy of the initial phase estimate, which requires expert user intervention. Further still, these phase unwrapping methods are computationally expensive, particularly in two-dimensions (2D) and higher, where the unwrapping problem becomes non-deterministic polynomial-time hard (NP-hard).
As such, other existing methods have been developed to overcome the inherent inaccuracies caused by the aforementioned tradeoffs in measuring inhomogeneities across multiple echoes. For example, some methods adopt a more statistical approach, but also rely on spatial regularization for robust mapping. Such smoothness assumptions may not be realistic as they do not account for small or abrupt variations common in MR images. Thus, such methods are particularly ill-suited for quantitative MR imaging, where physiological information is extracted from field maps. Ultimately, the performance of all these methods is subject to the trade-off inherent in the choice of the echo time spacing.
Therefore, it would be desirable to have a system and method for field map creation that is not subject to echo time spacing trade-offs and other inherent limitations of traditional methods, such as described above.